{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T17:00:20Z","timestamp":1791910820003,"version":"4.3.4"},"reference-count":130,"publisher":"American Chemical Society (ACS)","issue":"19","license":[{"start":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T00:00:00Z","timestamp":1790899200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T00:00:00Z","timestamp":1790899200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T00:00:00Z","timestamp":1790899200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People's Republic of China","doi-asserted-by":"publisher","award":["JYB2025XDXM309"],"award-info":[{"award-number":["JYB2025XDXM309"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22273038"],"award-info":[{"award-number":["22273038"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22403037"],"award-info":[{"award-number":["22403037"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22433001"],"award-info":[{"award-number":["22433001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"New Cornerstone Science Foundation"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,13]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Open-shell nanographenes (NGs) possess unique electronic properties that hold promise for next-generation carbon-based materials, yet their rational design is hampered by the lack of quantitative tools to predict their radical character. Empirical rules such as Clar\u2019s aromatic sextet rule and the Fries rule provide useful qualitative guides for closed-shell systems but inherently fail for open-shell NGs, where the ground state is better described as a resonance hybrid of closed-shell and open-shell structures. Here, we present a further development of the generalized valence-bond-based block-correlated coupled cluster (GVB-BCCC) theory and demonstrate its application in qualitative and quantitative predictions of the radical character in open-shell NGs. Four methodological advances are reported: (1) a systematic search procedure of multiple GVB solutions that enables the computational identification of distinct resonance structures (closed-shell, diradical, and tetraradical forms) through tailored initial orbital guesses; (2) the first implementation of GVB-BCCC4 for triplet ground states, extending the framework to systems with triplet ground states; (3) the first implementation of the unrelaxed one-particle density matrix for singlet GVB-BCCC4, enabling the extraction of natural orbital occupation numbers (NOONs) as a rigorous, quantitative measure of radical character directly from the GVB-BCCC4 wavefunction; and (4) the introduction of a relative local correlation energy (RLCE) index for evaluating local aromaticity in individual benzene-like rings. By exploiting the fact that distinct GVB solutions map to chemically intuitive resonance forms, our approach is able to identify the dominant resonance structure through accurate GVB-BCCC4 calculations on top of the respective GVB references. Critically, by comparing the uncorrelated GVB solutions with the fully correlated GVB-BCCC4 results, we can unambiguously determine whether the radical character of a given system originates from the \u03c0-skeleton topology (a resonance-driven effect) or from interpair electron correlation\u2500a distinction that remains inaccessible to empirical rules or conventional methods. Our approach is then applied to 11 representative NGs, including systems with up to 66 \u03c0 orbitals. The radical character indices from GVB-BCCC4 show excellent agreement with DMRG-CASCI reference data, while broken-symmetry DFT is found to be unreliable for systems with pronounced polyradical character. The singlet\u2013triplet energy gaps calculated at the GVB-BCCC4 level also agree well with available experimental values. This work establishes GVB-BCCC as a predictive tool for understanding the structure\u2013property relationships of open-shell systems and for guiding the rational design of carbon-based functional materials.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c01707","type":"journal-article","created":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T08:01:38Z","timestamp":1790928098000},"page":"10213-10226","source":"Crossref","is-referenced-by-count":0,"title":["Predicting the\nRadical Character of Open-Shell Nanographenes\nwith the GVB-Based Block-Correlated Coupled Cluster Theory"],"prefix":"10.1021","volume":"22","author":[{"given":"Xiaochuan","family":"Ren","sequence":"first","affiliation":[{"name":"Nanjing University , , ,","place":["Nanjing, People\u2019s Republic of China, 210023"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5198-3113","authenticated-orcid":true,"given":"Jingxiang","family":"Zou","sequence":"additional","affiliation":[{"name":"Huaqiao University , , , ,","place":["Xiamen, Fujian, People\u2019s Republic of China, 361021"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-5724-0603","authenticated-orcid":true,"given":"Jun","family":"Lin","sequence":"additional","affiliation":[{"name":"Nanjing University , , ,","place":["Nanjing, People\u2019s Republic of China, 210023"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cong","family":"Sun","sequence":"additional","affiliation":[{"name":"Nanjing University , , ,","place":["Nanjing, People\u2019s Republic of China, 210023"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7801-3643","authenticated-orcid":true,"given":"Wei","family":"Li","sequence":"additional","affiliation":[{"name":"Nanjing University , , ,","place":["Nanjing, People\u2019s Republic of China, 210023"]},{"name":"Guangxi University , , ,","place":["Nanning, People\u2019s Republic of China, 530004"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6756-057X","authenticated-orcid":true,"given":"Shuhua","family":"Li","sequence":"additional","affiliation":[{"name":"Nanjing University , , ,","place":["Nanjing, People\u2019s Republic of China, 210023"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,10,2]]},"reference":[{"key":"2026101310070113000_cit1","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1021\/cr068010r","article-title":"Graphenes as Potential Material for\nElectronics","volume":"107","author":"Wu","year":"2007","journal-title":"Chem. Rev."},{"key":"2026101310070113000_cit2","doi-asserted-by":"publisher","first-page":"5191","DOI":"10.1038\/s41467-021-25255-6","article-title":"A Contorted Nanographene\nShelter","volume":"12","author":"Wu","year":"2021","journal-title":"Nat. Commun."},{"key":"2026101310070113000_cit3","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1038\/s41428-018-0070-6","article-title":"Open-Shell Organic Semiconductors: An Emerging Class of Materials\nwith Novel Properties","volume":"50","author":"Huang","year":"2018","journal-title":"Polym. J."},{"key":"2026101310070113000_cit4","doi-asserted-by":"publisher","first-page":"2186","DOI":"10.1039\/C7CC09949E","article-title":"From Open-Shell\nSinglet Diradicaloids to Polyradicaloids","volume":"54","author":"Gopalakrishna","year":"2018","journal-title":"Chem.\nCommun."},{"key":"2026101310070113000_cit5","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1002\/jlac.19274540108","article-title":"U\u0308ber\nBicyclische Verbindungen Und Ihren Vergleich Mit Dem Naphtalin","volume":"454","author":"Fries","year":"1927","journal-title":"III. Mitteilung. Justus Liebigs Ann. Chem."},{"key":"2026101310070113000_cit6","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1002\/jlac.19355160117","article-title":"U\u0308ber\nTricyclische Verbindungen,\nin Denen Naphtalin Mit Einem Heterocyclus Anelliert Ist","volume":"516","author":"Fries","year":"1935","journal-title":"Justus Liebigs Ann. Chem."},{"key":"2026101310070113000_cit7","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/BF00549259","article-title":"Multiplicity\nof the Ground State of Large Alternant Organic Molecules with Conjugated\nBonds: (Do Organic Ferromagnetics Exist?)","volume":"47","author":"Ovchinnikov","year":"1978","journal-title":"Theor.\nChim. Acta"},{"key":"2026101310070113000_cit8","doi-asserted-by":"publisher","first-page":"11283","DOI":"10.1021\/jp021152e","article-title":"HOMO\u2013LUMO\nGap as an Index of Molecular Size and Structure for Polycyclic Aromatic\nHydrocarbons (PAHs) and Asphaltenes: A Theoretical Study. I","volume":"106","author":"Ruiz-Morales","year":"2002","journal-title":"J. Phys. Chem. 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Chem."},{"key":"2026101310070113000_cit14","doi-asserted-by":"publisher","DOI":"10.1002\/qua.25657","article-title":"Local Aromaticity\nand Aromatic Sextet Theory beyond\nClar","volume":"118","author":"Randic\u0301","year":"2018","journal-title":"Int. J. Quantum Chem."},{"key":"2026101310070113000_cit15","doi-asserted-by":"publisher","first-page":"1088","DOI":"10.1021\/acs.jpca.7b11095","article-title":"Predicting the Open-Shell Character of Polycyclic Hydrocarbons\nin Terms of Clar Sextets","volume":"122","author":"Trinquier","year":"2018","journal-title":"J. Phys. Chem. A"},{"key":"2026101310070113000_cit16","doi-asserted-by":"publisher","first-page":"1861","DOI":"10.1039\/jr9580001861","article-title":"378. 1: 12-2: 3-10:\n11-Tribenzoperylene","volume":"161","author":"Clar","year":"1958","journal-title":"J. Chem. Soc. 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J."},{"key":"2026101310070113000_cit26","doi-asserted-by":"publisher","first-page":"14054","DOI":"10.1021\/jacs.8b09075","article-title":"Superoctazethrene:\nAn Open-Shell Graphene-like Molecule Possessing Large Diradical Character\nbut Still with Reasonable Stability","volume":"140","author":"Zeng","year":"2018","journal-title":"J. Am.\nChem. Soc."},{"key":"2026101310070113000_cit27","doi-asserted-by":"publisher","first-page":"194107","DOI":"10.1063\/5.0029201","article-title":"Consistent Spin Decontamination of\nBroken-Symmetry Calculations of Diradicals","volume":"153","author":"David","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2026101310070113000_cit28","doi-asserted-by":"publisher","first-page":"13676","DOI":"10.1039\/D4SC03465A","article-title":"Prediction\nof the Ground State for\nIndenofluorene-Type Systems with Clar\u2019s \u03c0-Sextet Model","volume":"15","author":"George","year":"2024","journal-title":"Chem. Sci."},{"key":"2026101310070113000_cit29","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1038\/s41467-024-55556-5","article-title":"A Stable Open-Shell Peri-Hexacene with Remarkable Diradical Character","volume":"16","author":"Zhang","year":"2025","journal-title":"Nat. Commun."},{"key":"2026101310070113000_cit30","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1016\/0009-2614(75)80169-2","article-title":"The Electronic\nStructures of Biradicals in the Unrestricted Hartree-Fock Approximation","volume":"33","author":"Yamaguchi","year":"1975","journal-title":"Chem. Phys. Lett."},{"key":"2026101310070113000_cit31","doi-asserted-by":"publisher","first-page":"1789","DOI":"10.1021\/ja00526a005","article-title":"Occupation Numbers of Natural Orbitals\nas a Criterion\nfor Biradical Character. Different Kinds of Biradicals","volume":"102","author":"Doehnert","year":"1980","journal-title":"J. Am. Chem. Soc."},{"key":"2026101310070113000_cit32","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/BF00527740","article-title":"Extended Hartree-Fock\n(EHF) Theory of Chemical Reactions: III. Projected M\u00f8ller-Plesset\n(PMP) Perturbation Wavefunctions for Transition Structures of Organic\nReactions","volume":"73","author":"Yamaguchi","year":"1988","journal-title":"Theor. Chim. Acta"},{"key":"2026101310070113000_cit33","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1021\/acs.jpca.1c08661","article-title":"Quantitative\nResonance Theory Based on the Clar Sextet Model","volume":"126","author":"Wang","year":"2022","journal-title":"J. Phys. Chem. 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Chem."},{"key":"2026101310070113000_cit40","doi-asserted-by":"publisher","first-page":"2028","DOI":"10.1002\/jcc.25855","article-title":"Efficient\nOptimization of Natural\nResonance Theory Weightings and Bond Orders by Gram-based Convex Programming","volume":"40","author":"Glendening","year":"2019","journal-title":"J. Comput. Chem."},{"key":"2026101310070113000_cit41","doi-asserted-by":"publisher","first-page":"1625","DOI":"10.1021\/acs.jpca.5b12393","article-title":"Polyradical Character\nof Triangular Non-Kekule\u0301 Structures, Zethrenes, p -Quinodimethane-Linked Bisphenalenyl, and the Clar Goblet in Comparison:\nAn Extended Multireference Study","volume":"120","author":"Das","year":"2016","journal-title":"J. Phys. Chem.\nA"},{"key":"2026101310070113000_cit42","doi-asserted-by":"publisher","first-page":"18547","DOI":"10.1039\/C8CP02165A","article-title":"The Role of the Multiconfigurational\nCharacter of Nitronyl-Nitroxide in the Singlet\u2013Triplet Energy\nGap of Its Diradicals","volume":"20","author":"Barone","year":"2018","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026101310070113000_cit43","doi-asserted-by":"publisher","first-page":"2049","DOI":"10.1021\/acs.jpca.8b12440","article-title":"A Multireference Ab Initio Study\nof the Diradical Isomers of Pyrazine","volume":"123","author":"Scott","year":"2019","journal-title":"J. Phys.\nChem. A"},{"key":"2026101310070113000_cit44","doi-asserted-by":"publisher","first-page":"174121","DOI":"10.1063\/1.5092613","article-title":"CASSCF Linear\nResponse Calculations for Large Open-Shell Molecules","volume":"150","author":"Helmich-Paris","year":"2019","journal-title":"J. Chem. 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